1. Field of the Invention
The present invention generally relates to catalyst characterization and, more particularly, to determining the dispersion and metal particle size relationships of supported nanocatalysts employed in heterogeneous catalysis.
2. Description of the Related Art
The performance of catalysts is highly dependent on their physical and chemical properties. However, it is often difficult to directly measure physical and chemical properties of catalysts, especially those catalysts that contain metal particles whose average size is less than 100 nm (hereafter called “nanocatalysts”). Catalyst developers therefore rely on sophisticated characterization techniques to determine the physical and chemical properties and performance characteristics of new catalyst designs.
Dispersion and metal particle size distribution influence the performance of catalysts. Dispersion D is defined according to D=NTotS/NTotS, where NTotS is total amount of metal surface atoms and NTot is all metal atoms in the catalyst. Dispersion is an important property in catalysis because only atoms that are exposed to the surface are able to play a role in catalytic surface reactions. Catalyst metal particle size is also an important property because larger metal particles have less percentage of their atoms at the surface. As a consequence, a catalyst with smaller metal particles will usually outperform an equivalent amount of catalyst with identical metal concentration, but having larger metal particles.
The relationship between dispersion and metal particle size of catalysts has been studied in the publication by G. Bergeret and P. Gallezot, “Metal Particle Size and Dispersion Measurements,” Handbook of Heterogeneous Catalysis, Vol. 2, pp. 439-442, Wiley-VCH (1997). The model for the dispersion and metal particle size relationship proposed in that publication is as follows:
            D              B        -        G              =                  6        ×                  V          0                                      A          m                <        d        ⁢                  >          S                      ,where DB−G is the dispersion; V0 is the atomic volume; Am is the atomic area of the topmost surface atoms. Bergeret and Gallezot suggest to use Am=0.081 nm2, which gives an effective value for the low-index surfaces (111), (110) and (100). Note, however that the exact value of Am in practice is unknown for a given sample, and can deviate significantly from Am=0.081 nm2. <d>S is the surface-averaged metal particle size defined according to
            <      d      ⁢              >        s              =                  <                  d          3                >                    <                  d          2                >              ,where <d3> is the arithmetic average value of d3 and <d2> the arithmetic average value of d2.
The model noted above is deficient for several reasons. First, it does not work for small metal particles because it yields a dispersion value greater than 1.0. By definition, dispersion cannot be greater than 1.0. Second, the value of Am is typically assumed. In general, determining Am accurately is either very difficult (i.e., involves lengthy and laborious measurements of metal particle images) or not possible at all.